/*
 *                               POK header
 *
 * The following file is a part of the POK project. Any modification should
 * be made according to the POK licence. You CANNOT use this file or a part
 * of a file for your own project.
 *
 * For more information on the POK licence, please see our LICENCE FILE
 *
 * Please follow the coding guidelines described in doc/CODING_GUIDELINES
 *
 *                                      Copyright (c) 2007-2021 POK team
 */

/* e_jnf.c -- float version of e_jn.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#ifdef POK_NEEDS_LIBMATH

#include "math_private.h"
#include <libm.h>

static const float
#if 0
invsqrtpi=  5.6418961287e-01, /* 0x3f106ebb */
#endif
    two = 2.0000000000e+00, /* 0x40000000 */
    one = 1.0000000000e+00; /* 0x3F800000 */

static const float zero = 0.0000000000e+00;

float __ieee754_jnf(int n, float x) {
  int32_t i, hx, ix, sgn;
  float a, b, temp, di;
  float z, w;

  /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
   * Thus, J(-n,x) = J(n,-x)
   */
  GET_FLOAT_WORD(hx, x);
  ix = 0x7fffffff & hx;
  /* if J(n,NaN) is NaN */
  if (ix > 0x7f800000)
    return x + x;
  if (n < 0) {
    n = -n;
    x = -x;
    hx ^= 0x80000000;
  }
  if (n == 0)
    return (__ieee754_j0f(x));
  if (n == 1)
    return (__ieee754_j1f(x));
  sgn = (n & 1) & (hx >> 31); /* even n -- 0, odd n -- sign(x) */
  x = fabsf(x);
  if (ix == 0 || ix >= 0x7f800000) /* if x is 0 or inf */
    b = zero;
  else if ((float)n <= x) {
    /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
    a = __ieee754_j0f(x);
    b = __ieee754_j1f(x);
    for (i = 1; i < n; i++) {
      temp = b;
      b = b * ((float)(i + i) / x) - a; /* avoid underflow */
      a = temp;
    }
  } else {
    if (ix < 0x30800000) { /* x < 2**-29 */
      /* x is tiny, return the first Taylor expansion of J(n,x)
       * J(n,x) = 1/n!*(x/2)^n  - ...
       */
      if (n > 33) /* underflow */
        b = zero;
      else {
        temp = x * (float)0.5;
        b = temp;
        for (a = one, i = 2; i <= n; i++) {
          a *= (float)i; /* a = n! */
          b *= temp;     /* b = (x/2)^n */
        }
        b = b / a;
      }
    } else {
      /* use backward recurrence */
      /* 			x      x^2      x^2
       *  J(n,x)/J(n-1,x) =  ----   ------   ------   .....
       *			2n  - 2(n+1) - 2(n+2)
       *
       * 			1      1        1
       *  (for large x)   =  ----  ------   ------   .....
       *			2n   2(n+1)   2(n+2)
       *			-- - ------ - ------ -
       *			 x     x         x
       *
       * Let w = 2n/x and h=2/x, then the above quotient
       * is equal to the continued fraction:
       *		    1
       *	= -----------------------
       *		       1
       *	   w - -----------------
       *			  1
       * 	        w+h - ---------
       *		       w+2h - ...
       *
       * To determine how many terms needed, let
       * Q(0) = w, Q(1) = w(w+h) - 1,
       * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
       * When Q(k) > 1e4	good for single
       * When Q(k) > 1e9	good for double
       * When Q(k) > 1e17	good for quadruple
       */
      /* determine k */
      float t, v;
      float q0, q1, h, tmp;
      int32_t k, m;
      w = (n + n) / (float)x;
      h = (float)2.0 / (float)x;
      q0 = w;
      z = w + h;
      q1 = w * z - (float)1.0;
      k = 1;
      while (q1 < (float)1.0e9) {
        k += 1;
        z += h;
        tmp = z * q1 - q0;
        q0 = q1;
        q1 = tmp;
      }
      m = n + n;
      for (t = zero, i = 2 * (n + k); i >= m; i -= 2)
        t = one / (i / x - t);
      a = t;
      b = one;
      /*  estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
       *  Hence, if n*(log(2n/x)) > ...
       *  single 8.8722839355e+01
       *  double 7.09782712893383973096e+02
       *  long double 1.1356523406294143949491931077970765006170e+04
       *  then recurrent value may overflow and the result is
       *  likely underflow to zero
       */
      tmp = n;
      v = two / x;
      tmp = tmp * __ieee754_logf(fabsf(v * tmp));
      if (tmp < (float)8.8721679688e+01) {
        for (i = n - 1, di = (float)(i + i); i > 0; i--) {
          temp = b;
          b *= di;
          b = b / x - a;
          a = temp;
          di -= two;
        }
      } else {
        for (i = n - 1, di = (float)(i + i); i > 0; i--) {
          temp = b;
          b *= di;
          b = b / x - a;
          a = temp;
          di -= two;
          /* scale b to avoid spurious overflow */
          if (b > (float)1e10) {
            a /= b;
            t /= b;
            b = one;
          }
        }
      }
      b = (t * __ieee754_j0f(x) / b);
    }
  }
  if (sgn == 1)
    return -b;
  else
    return b;
}

float __ieee754_ynf(int n, float x) {
  int32_t i, hx, ix, ib;
  int32_t sign;
  float a, b, temp;

  GET_FLOAT_WORD(hx, x);
  ix = 0x7fffffff & hx;
  /* if Y(n,NaN) is NaN */
  if (ix > 0x7f800000)
    return x + x;
  if (ix == 0)
    return -one / zero;
  if (hx < 0)
    return zero / zero;
  sign = 1;
  if (n < 0) {
    n = -n;
    sign = 1 - ((n & 1) << 1);
  }
  if (n == 0)
    return (__ieee754_y0f(x));
  if (n == 1)
    return (sign * __ieee754_y1f(x));
  if (ix == 0x7f800000)
    return zero;

  a = __ieee754_y0f(x);
  b = __ieee754_y1f(x);
  /* quit if b is -inf */
  GET_FLOAT_WORD(ib, b);
  for (i = 1; i < n && (uint32_t)ib != 0xff800000; i++) {
    temp = b;
    b = ((float)(i + i) / x) * b - a;
    GET_FLOAT_WORD(ib, b);
    a = temp;
  }
  if (sign > 0)
    return b;
  else
    return -b;
}

#endif
